Will PDA work with BT wireless broadband?

If it's a wifi PDA it'll work with your wireless. Wireless is wireless. But some "wireless" is really cellphone internet, not wireless. Just make sure you're not getting a cellphone that doesn't have 802.11 internet connectivity - that's the wireless you want. (802.11N is the fastest, 802.11G or GS is still faster than you need, 802.11b is getting a bit old - there are internet connections that are faster - but it still works - at 11Mbps.)